Positive Solutions of {Delta <em>u</em>}+<em>u</em>^{(<em>n</em>+2)/(<em>n</em>-2)}=0 on Contractible Domains
Year: 1989
Journal of Partial Differential Equations, Vol. 2 (1989), Iss. 4 : pp. 83–88
Abstract
We show that there are bounded contractible domains in R^n, n ≥ 3, on which the Dirichlet problem for the equation Δu +u^{(n+2)/(n-2)} = 0 admit positive solutions. This result, combining with the well-known nonexistence result of Pohozaev, implies that geometry of the domains plays a crucial role in the solvability of the problem.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1989-JPDE-5845
Journal of Partial Differential Equations, Vol. 2 (1989), Iss. 4 : pp. 83–88
Published online: 1989-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 6